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Related Wheel Graphs and Its Locating Edge Domination Number

Last modified: 2017-07-09

#### Abstract

A subset $S$ of $E(G)$ is called an edge dominating set of $G$ if

every edge not in $S$ is adjacent to some edge in $S$. In this paper, we initiate to study a new concept in edge dominating set.

It is locating edge dominating set. A set $D \subseteq E$ is a locating

edge dominating set if every two edges $e_1, e_2 \in E(G) \setminus

D$ satisfy that $\emptyset \neq N(e_1) \cap D \neq N(e_2) \cap D \neq \emptyset$.

The location edge domination number $\gamma_L' (G)$ is the minimum cardinality of locating edge dominating set.

In this research, we analyze the locating edge dominating number of some related wheel graphs. We also analyze the upper bound of locating edge domination number.

every edge not in $S$ is adjacent to some edge in $S$. In this paper, we initiate to study a new concept in edge dominating set.

It is locating edge dominating set. A set $D \subseteq E$ is a locating

edge dominating set if every two edges $e_1, e_2 \in E(G) \setminus

D$ satisfy that $\emptyset \neq N(e_1) \cap D \neq N(e_2) \cap D \neq \emptyset$.

The location edge domination number $\gamma_L' (G)$ is the minimum cardinality of locating edge dominating set.

In this research, we analyze the locating edge dominating number of some related wheel graphs. We also analyze the upper bound of locating edge domination number.